SQL for Recursive Generation of Item Sequences

Oracle introduced recursive subquery factoring in version 11.2 of its database software. This offered a new way to write hierarchical queries, in addition to its Connect By clause, for navigating tree structures, such as an HR employee management hierarchy. It also offered the possibility to solve a wider range of problems using its more powerful form of recursion, including combinatorial optimization problems such as bin fitting (or knapsack) problems. I used the new technique to solve a number of such problems on this blog, starting in January 2013 with A Simple SQL Solution for the Knapsack Problem (SKP-1).

In this article, I focus on how the technique may be used to generate the sequences of items that form the basis of the solutions for the larger problems. In general we assume that we have a set of n items with unique identifiers, from which we want to form sequences of r items. Here are some definitions from Wikipedia to help us classify the different types of sequence possible:

Set (mathematics)

In mathematics, a set is a well-defined collection of distinct objects, considered as an object in its own right

Multiset

In mathematics, a multiset (aka bag or mset) is a modification of the concept of a set that, unlike a set, allows for multiple instances for each of its elements

Permutation

In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order

Combination

In mathematics, a combination is a selection of items from a collection, such that (unlike permutations) the order of selection does not matter

We can look for all sequences of r items from n, of four different types, based on the concepts above of:

  1. Set/Permutation – items may not repeat and order matters
  2. Set/Combination – items may not repeat and order does not matter
  3. Multiset/Permutation – items may repeat and order matters
  4. Multiset/Combination – items may repeat and order does not matter

Set/Permutation – items may not repeat and order matters

Suppose we have SP(r-1), the set of all (r-1)-tuples of type Set/Permutation, we can generate SP(r) by forming a set of new r-tuples from each (r-1)-tuple t(r-1)(j):

For each item i, add i on to t(r-1)(j):

t(r)(ij) = (t(r-1)(j), i)

Set/Combination – items may not repeat and order does not matter

Multiset/Permutation – items may repeat and order matters

Multiset/Combination – items may repeat and order does not matter

First we define the different types of sequences that are possible.

Initially we want to generate a set of all sequences satisfying certain generic conditions.
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Creating Open Source Projects for Database Code – Ireland Oracle User Group Conference 2020

***UPDATE, 12/04/2020: The conference was postponed indefinitely owing to COVID-19. My presentation will come out in some form at some time. Meanwhile I’m taking the opportunity to update some of my earlier Github projects with improved structure and READMEs.***

I’m speaking on ‘Creating Open Source Projects for Database Code’ at the Oracle User Group Ireland conference 2020 at 4pm on 12 March 2020 in the Gresham hotel, Dublin.

Here’s my abstract:

and here’s the agenda.

Here is a short Twitter thread with a couple of recordings with quick tips on GitHub READMEs: GitHub README tips.

I made a Twitter thread of recordings on my presentation at the 2019 conference: Writing Clean Code in PL/SQL and SQL – Twitter Recordings

#oug_ire #OUGIreland20






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Last October I gave a presentation on database unit testing with utPLSQL, Oracle Unit Testing with utPLSQL. I mentioned design patterns as a way of reducing the effort of building unit tests and outlined some strategies for coding them effectively.

In the current set of articles, I develop the ideas further, starting from the idea that all database APIs can be considered in terms of the axes:

  • direction (i.e. getter or setter, noting that setters can also ‘get’)
  • mode (i.e. real time or batch)

For each cell in the implied matrix, I construct an example API (or view) with specified requirements against Oracle’s HR demo schema, and use this example to construct a testing program with appropriate scenarios as a design pattern. Concepts and common patterns and anti-patterns in automated API testing are discussed throughout, and these are largely independent of testing framework used. However, the examples use my own lightweight independent framework that is designed to help avoid many API testing anti-patterns. The code is available on GitHub here, and includes both framework and design pattern examples: BrenPatF/db_unit_test

In this first example, I present a design pattern for web service ‘save’ procedures by means of a conceptual discussion, together with a working example of base code and unit test code for a procedure to save new employees in Oracle’s well-known HR demonstration schema. The working example can be used as a template for real use cases, and I believe can simplify the development process. It can also be used as a basis for comparing other unit testing frameworks, by implementing the same testing in those frameworks.

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